Answers
Problem 1
Triangle ABE is similar to triangle DCE. This is because we have two pairs of congruent corresponding angles.
angle AEB = angle DEC (vertical angles)angle ABE = angle DCE (alternate interior angles)Refer to the angle angle (AA) similarity theorem for more info.
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For the other pair of triangles, we don't have enough info to determine if they are similar or not. We have info about one pair of sides, and a pair of angles, but that's about it.
We need to know if JL is proportional to MO, and in the same ratio as KL & NO are, if we wanted to use the side angle side (SAS) similarity theorem.
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Summary:Triangle ABE is similar to triangle DCE by the AA (angle angle) similarity theoremWe don't have enough info to know if triangles JKL and MNO are similar or not.============================================================
Problem 2
Divide the corresponding sides
LN/PO = 30/15 = 2LN/OQ= 26/13 = 2ML/QP = 26/13 = 2We see the three ratios are equal to the same value (2) and that proves the triangles LNM and POQ are similar by the SSS (side side side) similarity theorem.
-------------------
Like before, we'll divide the corresponding sides
1st Rectangle: horizontal/vertical = 10/4 = 2.52ndRectangle: horizontal/vertical = 3/8 = 0.375We don't have a match. Let's try rotating the second rectangle so that the side '8' is horizontal, and the side '3' is vertical
1st Rectangle: horizontal/vertical = 10/4 = 2.52nd Rectangle: horizontal/vertical = 8/3 = 2.67 approximatelyWe don't have a match here either. There are other approaches we could take, but basically the two rectangles are not similar.
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Summary:Triangles LNM and POQ are similar by the SSS (side side side) similarity theorem.The rectangles are not similar.Related Questions
In a survey of 439 teenagers in the US, 14% said that they worked during their summer vacation. a) What is the Margin of Error for this sample proportion
Answers
Answer:
[tex]0.0166[/tex]
Step-by-step explanation:
Let the sample proportion be [tex]\hat{p}=0.14[/tex] and the sample size be [tex]n=439[/tex]:
[tex]\displaystyle \text{Margin of Error}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\text{Margin of Error}=\sqrt{\frac{0.14(1-0.14)}{439}}\\\\\text{Margin of Error}=\pm0.0166[/tex]
If you invest $18000 at an interest rate of 6.7%, compound quarterly, find the time needed for your investments to be worth $23,000
Answers
It will take approximately 5.5 years for the investment to be worth $23,000
Compound interestFrom the question, we are to determine when the investments will worth $23,000
Using the compound interest formula,
[tex]A = P (1+\frac{r}{n})^{nt}[/tex]
Where A is the amount
P is the principal
r is rate
n is the number of times it is compounded
and t is the time in years
From the given information,
A = $23000
P =$18000
r = 6.7%
n = 4
t = ?
Putting the parameters into the formula, we get
[tex]23000 = 18000(1+\frac{6.7}{100 \times 4})^{4t}[/tex]
[tex]\frac{23000}{18000} = (1.01675)^{4t}[/tex]
[tex]1.4375= (1.01675)^{4t}[/tex]
[tex]1.4375 = (1.0687)^{t}[/tex]
t = 5.46
t ≅ 5.5 years
Hence, it will take approximately 5.5 years for the investment to be worth $23,000
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Which is the equation of a hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0)? y squared over 40 minus x squared over 10 equals 1 y squared over 10 minus x squared over 15 equals 1 x squared over 10 minus y squared over 40 equals 1 x squared over 10 minus y squared over 15 equals 1
Answers
The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is [tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]
How to determine the equation of the hyperbola?The given parameters are:
Directrices at x = ±2 Foci at (5, 0) and (−5, 0)The foci of a hyperbola are represented as:
Foci = (k ± c, h)
The center is:
Center = (h,k)
And the directrix is:
Directrix, x = h ± a²/c
By comparison, we have:
k ± c = ±5
h = 0
h ± a²/c = ±2
Substitute h = 0 in h ± a²/c = ±2
0 ± a²/c = ±2
This gives
a²/c = 2
Multiply both sides by c
a² = 2c
k ± c = ±5 means that:
k ± c = 0 ± 5
By comparison, we have:
k = 0 and c = 5
Substitute c = 5 in a² = 2c
a² = 2 * 5
a² = 10
Next, we calculate b using:
b² = c² - a²
This gives
b² = 5² - 10
Evaluate
b² = 15
The hyperbola is represented as:
[tex]\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1[/tex]
So, we have:
[tex]\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1[/tex]
Evaluate
[tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]
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Geometry, Angles questions
Answers
Answer:
X= 82⁰
z= 82⁰
Step-by-step explanation:
for X:
we can use co-interior angles sum up to make 180 so,
x+ 98= 180
x= 180-90= 82⁰
for z, we can use either angles on a straight line or corresponding angles
using angles on a straight line,98 + z= 180
z= 180-98= 82⁰
using corresponding anglescorresponding angles are always equal and can be found in the F shape diagram when lines are parallel
therefore X and z are corresponding angles and since we found x= 82⁰ then z= 82⁰
Three teams, A, B and C, play in a competition.
games won by A: games won by B = 3:1
games won by B: games won by C = 4:3
Team B has won 10 games.
In total, how many games have the three teams won?
Answers
Answer:
47.5 games
Step-by-step explanation:
Finding A :
⇒ Games by A : Games by B = 3 : 1
⇒ Games by A : 10 = 3 : 1
⇒ Games by A = 30
==============================================================
Finding C :
⇒ Games by B / Games by C × Games by A / Games by B = 3 × 4/3
⇒ Games by A / Games by C = 4
⇒ Games by C = 30/4
⇒ Games by C = 7.5
==============================================================
Total games won :
⇒ Games by A + Games by B + Games by C
⇒ 30 + 10 + 7.5
⇒ 47.5 games
Make x the subject of the formula. y=(x-4)2+6 p.s the two is square
Answers
[tex]~~~~~~~~y = (x-4)^2 +6\\\\\implies (x-4)^2 = y-6 \\\\\implies x -4 = \pm\sqrt{y-6}\\\\\implies x = \pm\sqrt{y-6} +4[/tex]
If the sales price is 55.50, and the discount is 75%, what is the original price
Answers
Answer:
£74
Step-by-step explanation:
£55.50 = 75%
Find 1% of discounted price by dividing both sides by 75 :
£0.74 = 1%
Using 1%, multiply by 100% to find original price :
£74 = 100%
Check our answer :
£74 × 0.75 (75%) = £55.50 ✅
Hope this helped and brainliest please
Answer:
the original price is 416.25. because you take the 55.50 and times ... percent of discount is 75%, sale price is 55.50
Step-by-step explanation:
Translate the shape A four squares right and two squares up.
What are the coordinates of the vertices of the image?
will award brainliest to correct answer
Answers
Answer:
(5, 6)
Step-by-step explanation:
The original coordinate is (1, 1) (3, 1) (1, 4)
Translate four squares : (5, 1) (7, 1) (5, 4)
Translate two squares up: (5, 3) (7, 3) (5, 6)
The vertices of the image is (5, 6)
A fish tank is three-fourths full.
One-third of the water leaks out.
How full is the fish tank now?
Answers
Answer: [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
We will subtract the amount of water that leaked out from the amount of water originally in the fish tank.
[tex]\displaystyle \frac{3}{4} - \frac{1}{3} =\frac{3*3}{4*3} -\frac{1*4}{3*4} =\frac{9}{12} -\frac{4}{12}=\frac{5}{12}[/tex]
The fish tank is [tex]\frac{5}{12}[/tex] of the way full.
Which expression is equivalent to 3(8 + 7)?
Answers
Answer:
3 • 15
Step-by-step explanation:
Add 8 and 7 to factor out the equation, creating an equivalent expression.
The temperature was 73 degrees at noon. The temperature then changed because -2 degrees F each hour for 4 consecutive hours. What was the resulting temperature?
Answers
Step-by-step explanation:
73° starting temperature.
every hour -2° for 4 hours.
that means -2×4 = -8° during 4 hours.
so, the resulting temperature is
73 - 8 = 65°
Which expression is equivalent to
4^sqrt 6 / 3^sqrt2
Answers
Answer:
[tex]\dfrac{\sqrt[12]{55296} }{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}=\dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}}[/tex]
Multiply the numerator and denominator by [tex]2^{\frac{2}{3}}[/tex] :
[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}[/tex]
[tex]\textsf{Apply exponent rule to the denominator} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2^{\frac{1}{3}+\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}[/tex]
Rewrite 1/4 as 3/12 and 2/3 as 8/12 :
[tex]\implies \dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}=\dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^c \cdot b^c=(a \cdot b)^c:[/tex]
[tex]\implies \dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}=\dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}[/tex]
Simplify the operation in the parentheses:
[tex]\implies \dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}=\dfrac{(216\cdot 256)^\frac{1}{12}}{2}=\dfrac{(55296)^\frac{1}{12}}{2}[/tex]
[tex]\textsf{Finally, apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]
[tex]\implies \dfrac{(55296)^\frac{1}{12}}{2}=\dfrac{\sqrt[12]{55296} }{2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]
^b√a=a^1/b[tex]\\ \rm\Rrightarrow \dfrac{6^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]
6=2×3[tex]\\ \rm\Rrightarrow \dfrac{2^{\dfrac{1}{4}}3^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]
a^m÷a^n=a^m-n[tex]\\ \rm\Rrightarrow 2^{\dfrac{1}{4}-\dfrac{1}{3}}3^{\dfrac{1}{4}}[/tex]
[tex]\\ \rm\Rrightarrow 2^{\dfrac{-1}{12}}3^{\dfrac{1}{4}}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{1}{4}}}{2^{\dfrac{1}{12}}}[/tex]
Equalise exponential denominators[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{3}{12}}}{2^{\dfrac{1}{12}}}[/tex]
[tex]\\ \rm\Rrightarrow \left(\dfrac{3^3}{2}\right)^{\dfrac{1}{12}}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3}{2}}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3\times 2^82^3}{22^82^3}}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{27(256)(8)}{2^12}}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{6912(8)}}{2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{55296}}{2}[/tex]
What is the answer to (2 * 6)^3/2?
Answers
Answer:
864
Step-by-step explanation:
First, you multiply 2 and 6, so it's 12, and multiply it by 144, so it's 1728, and divide it by 2. Therefore, it's 864!
5. janelle got invited to a shopping spree with a friend and is supposed
to meet her at the mall at 4:00 p.m. when she has gone to the mall in the past,
she has noticed that it takes about two hours for her to travel to the mall.
she has also noticed that it takes her 30 minutes
to get ready before leaving her apartment. she concludes that she
needs to start getting ready at 0:30 p.m. this is an example of what?
inductive reasoning or deductive reasoning?
Answers
The given example is inductive reasoning.
What is inductive reasoning?The method of arriving at a conclusion based on a series of observations is known as inductive reasoning. It is not a valid method of proof in and of itself.
We have the information that. Janelle got invited to a shopping spree with a friend and is supposed to meet her at the mall at 4:00 p.m. when she has gone to the mall in the past,
she has noticed that it takes about two hours for her to travel to the mall. she has also noticed that it takes her 30 minutes to get ready before leaving her apartment. she concludes that she needs to start getting ready at 0:30 p.m.
The given information is giving us the series of the data like we are having a sequence of the timing at what time what she did so we have a series of observations here.
Therefore the given example is inductive reasoning.
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Suppose a bag contains 5 blocks. 3 red, 1 yellow and 1 green. what is the probability of selecting a red block?
Answers
answer is 3/5
since there are 3 red, there is a 3 blocks out of 5 blocks chance that a red block will chosen
can anyone help? i dont fully understand this
Answers
Answer:
It would be about 1/4
Step-by-step explanation:
Find the circumference of the circle. Use 3.14, Round to the nearest hundredth. the diameter is 20 ft
Answers
Answer:
62.8ft
Step-by-step explanation:
20/2=10 so 10*2=20 so 20*3.14=62.8
62.8
Answer:
314
Step-by-step explanation:
20/2 = 10
10 * 10 = 100
3.14 * 100 = 314
5x- 4y +2z when x= 8,y =3 and z =3
Answers
34
Step-by-step explanation:
=5x-4y+2z
=5×8-4×3+2×3
=40-12+6
=46-12
=34
Over what interval is the function in this graph constant?
W
OA. -3≤x≤2
OB. -4sxs-2
OC. -2≤x≤3
OD. -5≤x≤5
Answers
The function in this graph is constant in the range of -4 ≤x≤-2 , Option B is the correct answer.
What is a function ?A function is a mathematical statement which identifies relation between independent and dependent variable.
A graph is given
The graph will be considered constant when the y value is constant for any value of x
The value of y is constant in the range of
-4 ≤x≤-2
Therefore Option B is the correct answer.
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Exponential form of 5670
Answers
Answer:
The exponent form of 5670 is 5.67 × 103.
Step-by-step explanation:
you can also use this
it's pretty easy
https://calculator.name/decimal-to-scientific-notation/5670
Omar deposited $700 in his checking account but also wrote checks for $124.21 and $211.94. Assuming his original balance was $622.43, how much does he have in his account now?
show work
Answers
Answer:
$986.28
Step-by-step explanation:
$124.21 + $211.94 = $336.15
700 - 336.15 = 363.85
622.43 + 363.85 = 986.28
Help me out please asap
a boat sails due south from a port at a steady speed of 9 km/h.
the wind blows the boat due west at a speed of 3 km/h. how far is the boat from the port after 1 h?
give your answer to 1 decimal place.
Answers
The distance travelled by boat after 1 hour will be 10km.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
The distance will be calculated as:-
a²+b²=c²
9² + 3 ²= c ²
81+9 = c²
100 = c²
c = 10 km / hour
The distance travelled after one hour will be calculated as:-
Distance = Speed x Time
Distance = 10 x 1 = 10 Km
Therefore the distance travelled by boat after 1 hour will be 10km.
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Which graph shows a function where f(2)= 4?
Answers
From the curve given we can see that the graph that shows a function where f(2)= 4 is Graph A.
Equation of quadratic graphA quadratic graph is in form of a parabola opened upward or downward.
According to the question, we are to select a graph that has a coordinate (2, 4) on its curve.
To determine thus, we will locate the value of 2 on the x-axis and value of 4 on the y-intercept and trace whether the intersecting point is on the curve.
From the curve given we can see that the graph that shows a function where f(2)= 4 is Graph A.
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Your friend Dave has an obsession with hats! The only problem - it's an expensive habit but Dave doesn't seem to think so. You want to help show him exactly how much he is spending on hats. Each hat Dave buys costs \ (\$281). Write an expression to represent the total amount Dave spends on hats (\(h\)).
Answers
Answer:
281x
Step-by-step explanation:
each hat (x) cost 281. x times cost is total
Quincy's retirement party will cost $30 if he invites 10 guests. If there are 16 guests, how much will Quincy's retirement party cost? Solve using unit rates.
Answers
Answer:
$48
30/10 is equal to 3/1, 16 x 3 equals to 48.
Answer:$48
Step-by-step explanation:
$30/10p = $3 per person
3x6=18
18+30=48
Solve for x. Round to the nearest tenth, if necessary.
HELP ASAP PLEASE
Answers
Answer:
Step-by-step explanation:
Type the correct answer in the box. use numerals instead of words. the test to determine the presence of a certain virus in a pigeon is 97% accurate for a pigeon that has the virus and 99% accurate for a pigeon that does not have the virus. in a given population, 1.5% of the pigeons are infected. do not round your answer. the probability that a randomly selected pigeon gets an incorrect result is .
Answers
The probability that a randomly selected pigeon gets an incorrect result is; 0.0103
How to find the Probability?
We are told that;
1.5% pigeons are infected.
Inaccuracy of the test = 1 - 97% = 3%
1.5% of the pigeons are infected. Thus;
1 - 1.5% = 98.5% pigeons are un-infected.
Inaccuracy of test is 1 - 99% = 1% .
Thus;
0.03 and 0.01 are the probability of an error being made in infected and un-infected respectively.
Meanwhile, probability of infected and un-infected are 0.015 and 0.985 respectively.
Thus, the probability of a randomly chosen person gets an incorrect result = (0.03*0.015) + (0.985*0.01) = 0.0103
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A monument in the shape of a square pyramid was built in a park.
The four lateral faces of the pyramid will be painted. The cost and coverage information for regular paint and metallic paint are shown in the table. Both paint types will be used on the monument.
PAINT TYPE COST(dollars per gallon) GALLONS(sq ft per gallon)
regular $35 200
metallic $100 80
The regular paint will require 2 coats, and the metallic paint will require 1 coat. Both paint types are sold only by the gallon. Based on the table, what is the least amount of money that should be budgeted to paint the monument?
Answers
The least amount of money that should be budgeted to paint the monument is $1692.
Least amount of money that should be budgetedFirst step
Using Pythagorean theorem to find the surface area
Since POR is a right triangle
Hence:
PO=20
BR=12
OR=12
PR=√20²+12²
PR=400+144
PR=544
Area of PBC=1/2×24×√544
Area of PBC=12√544
Lateral surface area=4×12√544
Lateral surface area=48√544
Lateral surface area=1119.54²ft
Second step
Since regular paint is 2 coats 200 sq. ft per gallon
Hence:
Number of gallons=1119.54×2/200
Number of gallons= 11.2 gallons
11.2×35= 392
1119.54/80=13 gallons
13×100 =1300
Last step
Least amount=392+1300
Least amount= $1692
Therefore the least amount of money that should be budgeted to paint the monument is $1692.
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The area of a circle is 18.31cm2.
find the length of the radius rounded to 2 dp.
Answers
Answer:
Step-by-step explanation:
I really need help on this please anyone help
What Is the measure of angle A
Answers
sin A = 4/12 = 1/3
sin inv 1/3 = 19.47⁰
Answer:
option 4, 19.47°
Step-by-step explanation:
From angle A, the given side length are opposite and hypotenuse
SOH CAH TOA is
sinx = opposite / hypotenuse
cosx = adjacent / hypotenuse
tanx = opposite / adjacent
visual representation below
the given length fits the characteristic to use sin
sinA = opposite / hypotenuse
opposite = 4hypotenuse = 12sinA = 4 / 12
common facto is 4 it becomes sinA = 1 / 3
Apply trig inverse property,
x = arcsin(1/3)
x = 19.47122°